A NonPerturbative Definition of the Standard Models
Abstract
The Standard Models contain chiral fermions coupled to gauge theories. It has been a longstanding problem to give such gauged chiral fermion theories a quantum nonperturbative definition. By classification of quantum anomalies and symmetric invertible topological orders via a mathematical cobordism theorem for differentiable and triangulable manifolds, and the existence of symmetric gapped boundary for the trivial symmetric invertible topological orders, we propose that Spin(10) chiral fermion theories with Weyl fermions in 16dimensional spinor representations can be defined on a 3+1D lattice, and subsequently dynamically gauged to be a Spin(10) chiral gauge theory. As a result, the Standard Models from the 16nchiral fermion SO(10) Grand Unification can be defined nonperturbatively via a 3+1D local lattice model of bosons or qubits. Furthermore, we propose that Standard Models from the 15nchiral fermion SU(5) Grand Unification can also be realized by a 3+1D local lattice model of fermions.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1809.11171
 Bibcode:
 2018arXiv180911171W
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology;
 Quantum Physics
 EPrint:
 24 pages. Two columns. v3: Refinement with detailed discussions. Appendices include viewpoints from perturbative local anomalies and nonperturbative global anomalies (e.g. arXiv:1810.00844, SU(2) = Spin(3) $\subset$ Spin(10)), and co/bordism theories (e.g. $\Omega_{D}^{{(\mathrm{Spin}(D) \times \mathrm{Spin}(10))}/{\mathbb{Z}_2^f}}$)